15 MAY 2013
CORRESPONDENCE
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Reply to ‘‘Comments on ‘Erroneous Model Field Representations in Multiple
Pseudoproxy Studies: Corrections and Implications’’’*
JASON E. SMERDON AND ALEXEY KAPLAN
Lamont-Doherty Earth Observatory, Columbia University, Palisades, New York
DANIEL E. AMRHEIN
Massachusetts Institute of Technology–Woods Hole Oceanographic Institution Joint Program in Oceanography,
Cambridge, Massachusetts
(Manuscript received 29 March 2012, in final form 9 January 2013)
ABSTRACT
The commenters confirm the errors identified and discussed in Smerdon et al., which either invalidated or
required the reinterpretation of quantitative results from pseudoproxy experiments presented or used in
several earlier papers. These errors have a strong influence on the spatial skill assessments of climate field
reconstructions (CFRs), despite their small impacts on skill statistics averaged over the Northern Hemisphere. On the basis of spatial performance and contrary to the claim by the commenters, the Regularized
Expectation Maximization method using truncated total least squares (RegEM-TTLS) cannot be considered a preferred CFR technique. Moreover, distinctions between CFR methods in the context of the discussion in the original paper are immaterial. Continued investigations using accurately described and
faithfully executed pseudoproxy experiments are critical for further evaluation and improvement of CFR
methods.
Rutherford et al. (2013, hereinafter R13) confirm the
errors that were identified and discussed in Smerdon
et al. (2010, hereinafter S10). These errors were associated with the processing of the millennium-length
National Center for Atmospheric Research (NCAR)
Community Climate System Model, version 1.4 (CCSM1.4)
(Ammann et al. 2007), and the global Hamburg Ocean
Primitive Equation (ECHO-G) (González-Rouco et al.
2003) simulations by Mann et al. (2005) and Mann et al.
(2007, hereinafter M07). R13 also clarify that related papers published after M07 were not affected by the errors described in S10. This is an important clarification.
Below we respond to several additional arguments raised
by R13.
* Lamont-Doherty Earth Observatory Contribution Number
7669.
Corresponding author address: Jason E. Smerdon, LamontDoherty Earth Observatory, Columbia University, 61 Route 9W,
P.O. Box 1000, Palisades, NY 10964.
E-mail: [email protected]
DOI: 10.1175/JCLI-D-12-00165.1
Ó 2013 American Meteorological Society
R13 emphasize a distinction between the two versions
of the Regularized Expectation Maximization (RegEM)
method (Schneider 2001). They imply that RegEM using truncated total least squares (RegEM-TTLS) is a
better climate field reconstruction (CFR) method than
RegEM using ridge regression (RegEM-Ridge), the
latter of which was used by S10 to illustrate some consequences of the data-processing errors. We first note
that any CFR method could have been used to demonstrate the errors discovered by S10, making methodological distinctions in this context immaterial. Second,
it is true that RegEM-TTLS has been shown in pseudoproxy studies to better reconstruct the Northern
Hemisphere (NH) mean (see Smerdon 2012 for a review), but both of the RegEM methods are meant to
reconstruct temperature fields. Spatial reconstruction
skill therefore is a fundamental measure of their performance. To date, the only comprehensive comparisons of the spatial skill of multiple methods for global
temperature CFRs did not find RegEM-TTLS to be a
clear frontrunner (Smerdon et al. 2011; Li and Smerdon
2012). To the contrary, RegEM-TTLS performs similarly to other multivariate regression methods in several
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spatial skill metrics, and all of the evaluated methods
have important spatial errors. The advocacy of one multivariate linear CFR method over another is therefore
premature.
R13 also claim that similar results are obtained from
pseudoproxy experiments using the correctly and incorrectly oriented CCSM1.4 fields. This point requires
qualification: the statistics reported in lines three and
four of R13’s Table 1 are similar only because they are
NH averages. The spatial performance of RegEMTTLS and other CFR methods is nevertheless strongly
dependent on the distribution of the pseudoproxy
network (Smerdon et al. 2011; Werner et al. 2013;
Annan and Hargreaves 2012). Any perceived similarity
between results presented by Mann et al. (2005), M07,
and R13 therefore only holds for NH-averaged statistics, while regional skill statistics (e.g., for Ni~
no-3)
would expose important differences between experiments with correct and incorrect sampling as demonstrated in S10.
Maintaining consistent and correctly documented records of pseudoproxy tests is critical for evaluating CFR
methods. The advantage of such tests lies in their ability
to serve as common testbeds on which reconstruction
methods can be systematically evaluated and compared
[see Smerdon (2012) for a review]. This advantage can
only be realized if pseudoproxy experiments are accurately described and correctly executed. Timely corrections to pseudoproxy tests are therefore vital for avoiding
the perpetuation of errors and inconsistencies in the
published literature.
Acknowledgments. This research was supported in
part by the National Science Foundation by Grant ATM0902436 and by the National Oceanic and Atmospheric
Administration by Grant NA07OAR4310060.
VOLUME 26
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